Which expression is equivalent?

What is the lateral area of a right cylinder if the radius of the base is 12 mm and the altitude of the cylinder is 5 times the

lakkis [162]

The lateral area of a cylinder is given by:
Area=πrl+2πr^2
radius,r=12 mm
length,l=5*12=60mm
therefore the lateral area will be:
Area=π*12*60
Area=2,261.95 mm^2
The area of the bases will be:
A=2*π*12^2=904.78 mm^s
The lateral area will be:
2,261.95+904.78
=3,166.73
=3167 mm^2

5 0

3 years ago

Geometry page 1 help please !

victus00 [196]

Answer:

16) $y=\frac{1}{4}x +5$

17) y = -x - 4

18) y = -2x - 1

19) y = -2x

20) $y=\frac{-5}{3} -3$

Step-by-step explanation:

With the two points you find the slope using $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Then using that slope, plug the slope in with one of the points values of x and y into the point slope formula, and smiplify that into the y-intercept formula.

6 0

3 years ago

To make fruit punch for a party, we need 4 1⁄2 gallons of ginger ale, 1 gallon of strawberry juice, 2 3⁄4 gallons of frozen oran

lina2011 [118]

For this case we convert the mixed numbers to fractions:

$4 \frac {1} {2} = \frac {2 * 4 + 1} {2} = \frac {9} {2}\\2 \frac {3} {4} = \frac {4 * 2 + 3} {4} = \frac {11} {4}$

Now we add the fractions:

$\frac{9} {2}+1+ \frac {11} {4} + \frac {1} {8} =$

We find the least common multiple of the denominators. The l.c.m is 8, then we divide by each denominator and multiply the result by each numerator.

$\frac {36 + 8 + 22 + 1} {8} =\\\frac {67} {8} =$

8,375

Thus, the punch recipe implies 8.375 gallons. If we convert to a mixed number we have:

$8 \frac {3} {8}$ gallons

Answer:

$8 \frac {3} {8}$ gallons

4 0

2 years ago

Use the laws of Sines and law of cosines to find missing dimensions

Andrei [34K]

Answer:

A) ERROR

B) ∠C = 26°

Step-by-step explanation:

Houston, We have a problem!!! too much information

If we had a legit triangle, the law of sines would hold

19/sin138 = 8/sin20

28.395 = 23.390

as this is NOT an equality, the triangle does not exist as described.

IF it did, we'd get different results depending on which set we used

∠F = 180 - 138 - 20 = 22°

Law of sines

19/sin138 = DE/sin22 ⇒ DE = 19sin22/sin138 = 10.63697...

or

8/sin20 = DE/sin22 ⇒ DE = 8sin22/sin20 = 8.762211...

If we attempt to use Law of cosines

DE² = 19² + 8² - 2(19)(8)cos22 = 11.9639...

so really none is correct because we attempt to use trig calculations to a non-triangle.

12) AC² = 15² + 19² - 2(15)(19)cos120

AC = 29.51270...

29.51270 / sin120 = 15/sinC

C = arcsin(15sin120/29.51270) = 26.1142... 26°

6 0

2 years ago

Read 2 more answers

A projectile is launched into the air. The function h(t) = –16t2 + 32t + 128 gives the height, h, in feet, of the projectile t s

Zinaida [17]

Answer:

t = 4 seconds

Step-by-step explanation:

The height of the projectile after it is launched is given by the function :

$h(t)=-16t^2+32t+128$

t is time in seconds

We need to find after how many seconds will the projectile land back on the ground. When it land, h(t)=0

So,

$-16t^2+32t+128=0$

The above is a quadratic equation. It can be solved by the formula as follows :

$t=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}$

Here, a = -16, b = 32 and c = 128

$t=\dfrac{-32\pm \sqrt{(32)^2-4\times (-16)(128)} }{2\times (-16)}\\\\t=\dfrac{-32+ \sqrt{(32)^2-4\times (-16)(128)} }{2\times (-16)}, \dfrac{-32\- \sqrt{(32)^2-4\times (-16)(128)} }{2\times (-16)}\\\\t=-2\ s\ \text{and}\ 4\ s$

Neglecting negative value, the projectile will land after 4 seconds.

4 0

3 years ago

Which expression is equivalent? - 5(2x -3y +4)