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3 years ago

I need help , please

Mathematics

1 answer:

bezimeni [28]3 years ago

4 0

To determine which statement is true, first find the measure of the third interior angle. You can do that by subtracting the two known interior angle measures from 180, since interior angle measures of all triangles add to equal 180 degrees.

180 - 65 - 57 = 58

The measure of the third interior angle is 58°.

Now, the largest side of triangle is opposite its largest interior angle; that means the largest side of this triangle is the side opposite the angle that measures 65° - the side representing swim distance. This is true for the middle and smallest sides as well - they're opposite the middle and smallest interior angles. The following shows the sides from largest to smallest as they correspond to angle measures from largest to smallest.

65° = swim
58° = bike
57° = run

Now to finally determine which statement is true.
Statement A is false because run distance is the smallest distance of all three distances.
Statement B is false because, as we've said, run distance is the smallest distance.
Statement C is false because swim distance is greater than bike distance.

That means that the correct answer is D - the bike distance is greater than the run distance.

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2sinx / cos3x = tan3x - tanx -verify the identity-

scoundrel [369]

Answer:

cos3x+tan3x=0

⟹cos3x=−tan3x

⟹cos3x=−sin3xcos3x

⟹cos23x=−sin3x

⟹1−sin23x=−sin3x

⟹sin23x−sin3x−1=0

This is a quadratic equation in sin3x.

sin3x=−(−1)±(−1)2−4×1×(−1)−−−−−−−−−−−−−−−−−√2×1

sin3x=1±5–√2

If x takes real values, the upper sign must be rejected.

sin3x=1−5–√2

⟹3x=nπ+(−1)nsin−11−5–√2

⟹x=13[nπ+(−1)nsin−11−5–√2]

Step-by-step explanation:

Hope this kind of helps

6 0

2 years ago

The clerk at the checkout counter earned $350 in 25 hours.

REY [17]

Answer: 14 a hour

Step-by-step explanation:

3 0

3 years ago

In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 3.0 m/s up a 22.0° inclined track

Aloiza [94]

Answer:

Approximately $0.31\; \rm m$ , assuming that $g = 9.81\; \rm N \cdot kg^{-1}$ .

Step-by-step explanation:

Initial kinetic energy of the sled and its passenger:

$\begin{aligned}\text{KE} &= \frac{1}{2}\, m \cdot v^{2} \\ &= \frac{1}{2} \times 14\; \rm kg \times (3.0\; \rm m\cdot s^{-1})^{2} \\ &= 63\; \rm J\end{aligned}$ .

Weight of the slide:

$\begin{aligned}W &= m \cdot g \\ &= 14\; \rm kg \times 9.81\; \rm N \cdot kg^{-1} \\ &\approx 137\; \rm N\end{aligned}$ .

Normal force between the sled and the slope:

$\begin{aligned}F_{\rm N} &= W\cdot \cos(22^{\circ}) \\ &\approx 137\; \rm N \times \cos(22^{\circ}) \\ &\approx 127\; \rm N\end{aligned}$ .

Calculate the kinetic friction between the sled and the slope:

$\begin{aligned} f &= \mu_{k} \cdot F_{\rm N} \\ &\approx 0.20\times 127\; \rm N \\ &\approx 25.5\; \rm N\end{aligned}$ .

Assume that the sled and its passenger has reached a height of $h$ meters relative to the base of the slope.

Gain in gravitational potential energy:

$\begin{aligned}\text{GPE} &= m \cdot g \cdot (h\; {\rm m}) \\ &\approx 14\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \times h\; {\rm m} \\ & \approx (137\, h)\; {\rm J} \end{aligned}$ .

Distance travelled along the slope:

$\begin{aligned}x &= \frac{h}{\sin(22^{\circ})} \\ &\approx \frac{h\; \rm m}{0.375}\end{aligned}$ .

The energy lost to friction (same as the opposite of the amount of work that friction did on this sled) would be:

$\begin{aligned} & - (-x)\, f \\ = \; & x \cdot f \\ \approx \; & \frac{h\; {\rm m}}{0.375}\times 25.5\; {\rm N} \\ \approx\; & (68.1\, h)\; {\rm J}\end{aligned}$ .

In other words, the sled and its passenger would have lost (approximately) $((137 + 68.1)\, h)\; {\rm J}$ of energy when it is at a height of $h\; {\rm m}$ .

The initial amount of energy that the sled and its passenger possessed was $\text{KE} = 63\; {\rm J}$ . All that much energy would have been converted when the sled is at its maximum height. Therefore, when $h\; {\rm m}$ is the maximum height of the sled, the following equation would hold.

$((137 + 68.1)\, h)\; {\rm J} = 63\; {\rm J}$ .

Solve for $h$ :

$(137 + 68.1)\, h = 63$ .

$\begin{aligned} h &= \frac{63}{137 + 68.1} \approx 0.31\; \rm m\end{aligned}$ .

Therefore, the maximum height that this sled would reach would be approximately $0.31\; \rm m$ .

7 0

3 years ago

What is the solution for the equation -15=5(3y-10)-5y

marissa [1.9K]

Answer:

$\Large\boxed{\sf{y=\dfrac{7}{2} }}$

Step-by-step explanation:

Isolate the variable of y from one side of the equation.

-14=5(3y-10)-5y

First, switch sides.

$\sf{5\left(3y-10\right)-5y=-15}$

Use the distributive property.

DISTRIBUTIVE PROPERTY:

A(B-C)=AB-AC

5(3y-10)

Multiply by expand.

5*3y=15y

5*10=50

15y-50-5y

15y-5=10y

= 10y-50

10y-50=-15

Add by 50 from both sides.

10y-50+50=-15+50

Solve.

10y=35

Then, you divide by 10 from both sides.

10y/10=35/10

Solve.

Divide the numbers from left to right.

35/10=7/2

y=7/2

Divide is another option.

7/2=3.5

$\Longrightarrow: \boxed{\sf{y=\dfrac{7}{2}}}$

Therefore, the correct answer is y=7/2.

I hope this helps. Let me know if you have any questions.

7 0

2 years ago

Algebra find the unknown digit to make each statement true 2.48>2.4 1>2.463

valentina_108 [34]

We have 2.48>2.4 1>2.463. If we insert a '7' between that 4 and 1, we get:

2.48 > 2.471 >2.463, and this is true.

8 0

3 years ago