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3 years ago

What is a factor of both 28 and 49

Mathematics

1 answer:

sdas [7]3 years ago

5 0

Factor 28 and 49

28
1*14
1*2*7

49
7*7

7 is the answer

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Is -6.333 greater less equal to -6.375

Leviafan [203]

6.375 is greater than 6.333

3 0

3 years ago

Read 2 more answers

Use your calculator to find the value of the trigonometric ratio rounded to 4 decimal places.

valentinak56 [21]

Answer:

0.6820

Step-by-step explanation:

Given data

Angle= 47°

Hence we want to find

cos 47°

From calculator

cos 47°=0.681998

to 4 dp

0.6820

4 0

3 years ago

You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B o

anyanavicka [17]

Answer:

$x =\dfrac{45 \sqrt{6}}{ 2}$

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

$\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}$

In order to estimate the point along the shore, x meters from B, the runner should stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

= $\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0$

$-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0$

$\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}$

$\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}$

$\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}$

$\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}$

squaring both sides; we get

$\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}$

$\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}$

By cross multiplying; we get

$49x^2 = 25(54^2+x^2)$

$49x^2 = 25 \times 54^2+ 25x^2$

$49x^2-25x^2 = 25 \times 54^2$

$24x^2 = 25 \times 54^2$

$x^2 = \dfrac{25 \times 54^2}{24}$

$x =\sqrt{ \dfrac{25 \times 54^2}{24}}$

$x =\dfrac{5 \times 54}{\sqrt{24}}$

$x =\dfrac{270}{\sqrt{4 \times 6}}$

$x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}$

$x =\dfrac{45 \sqrt{6}}{ 2}$

8 0

3 years ago

Emily estimated that there were 315 students at a soccer game the actual number of students at the game with 350 what was the pe

Readme [11.4K]

Answer:

About 11.10 Percent off. The change from 315 to 350 was an increase

Step-by-step explanation:

4 0

3 years ago

Carrie borrowed $960 in interest free to pay for a car repair. She will pay $120 monthly until the loan is paid off. How many mo

astraxan [27]

Answer:

It will take Carrie 8 months to pay off the loan

Step-by-step explanation:

Step 1: Determine the expression for total amount to be paid

T=m×n

where;

T=total amount to be payed

m=total payments per month

n=number of payments to be made

In our case;

T= $960

m= $120

n=unknown

replacing;

960=120×n

120 n=960

n=960/120

n=8 months

It will take Carrie 8 months to pay off the loan

6 0

3 years ago