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2 years ago

Find the measure of

Mathematics

2 answers:

Klio2033 [76]2 years ago

6 0

Answer:

See below ~

Step-by-step explanation:

The total internal measure is 360°.

154° + 60° + 86 + ∠STP + ∠TUP = 360°
2∠STP + 300 = 360°
2∠STP = 60°
∠STP = ∠TUP = 30°

Finding ∠SPQ (clockwise):

2∠STP + 86°
2(30) + 86
146°

Finding ∠SPQ (counterclockwise) :

360° - 146°
214°

Lady_Fox [76]2 years ago

3 0

Answer:

Angles around a point sum to 360°

⇒ ∠SPT + ∠TPU + 86° + 60° + 154° = 360°

⇒ ∠SPT + ∠TPU = 60°

Therefore:

∠SPQ clockwise = ∠SPT + ∠TPU + 86°

= 60° + 86°

= 146°

∠SPQ anticlockwise = 60° + 154°

= 214°

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Find the total surface area of this cone.

3241004551 [841]

Answer:

Step-by-step explanation:

Total surface area of a cone is given by the expression,

SA = πrl + B

Here, r = Radius of the circular base

l = slant height

B = Surface area of the base

Surface area of the circular base = πr²

= π(5)²

= 25π cm²

Slant height 'AC' = $\sqrt{AB^2+BC^2}$

= $\sqrt{h^2+r^2}$

= $\sqrt{5^2+(12)^2}$

= 13 cm

Substitute the values in the expression of surface area,

SA = π(5)(13) + 25π

= 65π + 25π

= 90π cm²

Therefore, SA = 90π cm² will be the answer.

6 0

3 years ago

Find the perimeter of the rectangle .23m 27m

lions [1.4K]

Answer:

If the width is 23 meters, the perimeter of the rectangle is 100 meters, or if the width of the rectangle is 0.23 meters, the perimeter is 54.46 meters.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Length of the rectangle = 27 meters

Width of the rectangle = 23 meters or 0.23 meters (it's not clear)

2. We will calculate the perimeter for any of the two possible values of the width of the rectangle, this way:

Perimeter of the rectangle = 2 * Length + 2 * Width

Replacing with the values we know:

Perimeter of the rectangle = 2 * 27 + 2 * 23

Perimeter of the rectangle = 54 + 46 = 100 meters

Perimeter of the rectangle = 2 * 27 + 2 * 0.23

Perimeter of the rectangle = 54 + 0.46 = 54.46 meters

7 0

3 years ago

A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle.

Lesechka [4]

So we know that the formula for the area of a rectangle is $A = lw$ .
Now both the length and width of the rectangle increase at 3 km/s, therefore, $A(t) = (3t+l)*(3t+w). Since the initial length = initial width = 4 km, then the initial area = 16 [tex]km^2$ . We want to know the time when the area is four times its original area, therefore, our new formula is: $4A(t) = (3t+l)*(3t+w)$ . Plugging in our known values we have:

$64 [km^2] = (3t + 4 [km])*(3t + 4 [km])$
$t = \frac{4}{3} s$

The area is four times its original area after \frac{4}{3} s[/tex].

6 0

4 years ago

A cake is removed from a 310°F oven and placed on a cooling rack in a 72°F room. After 30 minutes the cake's temperature is 220°

Fynjy0 [20]

Answer:

The time is 135 min.

Step-by-step explanation:

For this situation we are going to use Newton's Law of Cooling.

Newton’s Law of Cooling states that the rate of temperature of the body is proportional to the difference between the temperature of the body and that of the surrounding medium and is given by

$T(t)=C+(T_0-C)e^{kt}$

where,

C = surrounding temp

$T(t)$ = temp at any given time

t = time

$T_0$ = initial temp of the heated object

k = constant

From the information given we know that:

Initial temp of the cake is 310 °F.
The surrounding temp is 72 °F.
After 30 minutes the cake's temperature is 220 °F.

We want to find the time, in minutes, since the cake's removal from the oven, at which its temperature will be 100°F.

To do this, first, we need to find the value of k.

Using the information given,

$220=72+(310-72)e^{k\cdot 30}\\\\72+238e^{k30}=220\\\\238e^{k30}=148\\\\e^{k30}=\frac{74}{119}\\\\\ln \left(e^{k\cdot \:30}\right)=\ln \left(\frac{74}{119}\right)\\\\k\cdot \:30=\ln \left(\frac{74}{119}\right)\\\\k=\frac{\ln \left(\frac{74}{119}\right)}{30}$

$T(t)=72+(310-72)e^{(\frac{\ln \left(\frac{74}{119}\right)}{30}\cdot t)}$

Next, we find the time at which the cake's temperature will be 100°F.

$100=72+(310-72)e^{(\frac{\ln \left(\frac{74}{119}\right)}{30}\cdot t)}\\72+238e^{\frac{\ln \left(\frac{74}{119}\right)}{30}t}=100\\238e^{\frac{\ln \left(\frac{74}{119}\right)}{30}t}=28\\e^{\frac{\ln \left(\frac{74}{119}\right)}{30}t}=\frac{2}{17}\\\ln \left(e^{\frac{\ln \left(\frac{74}{119}\right)}{30}t}\right)=\ln \left(\frac{2}{17}\right)\\\frac{\ln \left(\frac{74}{119}\right)}{30}t=\ln \left(\frac{2}{17}\right)\\t=\frac{30\ln \left(\frac{2}{17}\right)}{\ln \left(\frac{74}{119}\right)}\approx 135.1$

4 0

3 years ago

Please help me please will give brainliest do only 23 ,25, by factoring

yaroslaw [1]

9514 1404 393

Answer:

23) x = ±3i, ±√2

26) x = 4/3, (-2/3)(1 ± i√3)

Step-by-step explanation:

23) Put in standard form to make factoring easier.

x^4 +7x^2 -18 = 0

(x^2 +9)(x^2 -2) = 0 . . . . factors in integers

Using the factoring of the difference of squares, you can continue to get linear factors in complex and irrational numbers:

(x -3i)(x +3i)(x -√2)(x +√2) = 0

x = ±3i, ±√2

___

26) This will be the difference of cubes after you remove the common factor.

81x^3 -192 = 0

3(27x^3 -64) = 0

(3x -4)(9x^2 +12x +16) = 0 . . . . . factor the difference of cubes

The complex roots of the quadratic can be found using the quadratic formula.

x = (-12 ±√(12^2 -4(9)(16)))/(2(9)) = (-12 ±√-432)/18 = -2/3 ± √(-4/3)

Then the three solutions to the equation are ...

x = 4/3, (-2/3)(1 ± i√3)

5 0

3 years ago